The Confrontation Between General Relativity and Experiment

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1 Space Sci Rev DOI /s The Confrontation Between General Relativity and Experiment C.M. Will Received: 13 November 2008 / Accepted: 20 May 2009 Springer Science+Business Media B.V Abstract We review the experimental evidence for Einstein s general relativity. A variety of high precision null experiments confirm the Einstein Equivalence Principle, which underlies the concept that gravitation is synonymous with spacetime geometry, and must be described by a metric theory. Solar system experiments that test the weak-field, post-newtonian limit of metric theories strongly favor general relativity. Binary pulsars test gravitational-wave damping and aspects of strong-field general relativity. During the coming decades, tests of general relativity in new regimes may be possible. Laser interferometric gravitational-wave observatories on Earth and in space may provide new tests via precise measurements of the properties of gravitational waves. Future efforts using X-ray, infrared, gamma-ray and gravitational-wave astronomy may one day test general relativity in the strong-field regime near black holes and neutron stars. Keywords General relativity Gravitational experiments 1 Introduction During the late 1960s, it was frequently said that the field of general relativity is a theorist s paradise and an experimentalist s purgatory. The field was not without experiments, of course: Irwin Shapiro, then at MIT, had just measured the relativistic retardation of radar waves passing the Sun (an effect that now bears his name), Robert Dicke of Princeton was claiming that the Sun was flattened by rotation in an amount whose effects on Mercury s perihelion advance would put general relativity afoul of experiment, and Joseph Weber of the University of Maryland was busy building gravitational wave antennas out of massive C.M. Will ( ) Department of Physics, McDonnell Center for the Space Sciences, Washington University, St. Louis, MO, USA cmw@wuphys.wustl.edu C.M. Will Gravitation et Cosmologie, Institut d Astrophysique de Paris, 98 bis Bd. Arago, Paris, France

2 C.M. Will aluminum cylinders. Nevertheless the field was dominated by theory and by theorists. The field circa 1970 seemed to reflect Einstein s own attitudes: although he was not ignorant of experiment, and indeed had a keen insight into the workings of the physical world, he felt that the bottom line was the theory. As he once famously said, if experiment were to contradict the theory, he would have felt sorry for the dear Lord. Since that time the field has been completely transformed, and today experiment is a central, and in some ways dominant component of gravitational physics. The breadth of current experiments, ranging from tests of classic general relativistic effects, to searches for short-range violations of the inverse-square law, to a space experiment to measure the relativistic precession of gyroscopes, attest to the ongoing vigor of experimental gravitation. The great progress in testing general relativity during the latter part of the 20th century featured three main themes: The use of advanced technology. This included the high-precision technology associated with atomic clocks, laser and radar ranging, cryogenics, and delicate laboratory sensors, as well as access to space. The development of general theoretical frameworks. These frameworks allowed one to think beyond the narrow confines of general relativity itself, to analyse broad classes of theories, to propose new experimental tests and to interpret the tests in an unbiased manner. The synergy between theory and experiment. To illustrate this, one needs only to note that the LIGO-Virgo Scientific Collaboration, engaged in one of the most important general relativity investigations the detection of gravitational radiation consists of over 700 scientists. This is big science, reminiscent of high-energy physics, not general relativity! Today, because of its elegance and simplicity, and because of its empirical success, general relativity has become the foundation for our understanding of the gravitational interaction. Yet modern developments in particle theory suggest that it is probably not the entire story, and that modifications of the basic theory may be required at some level. String theory generally predicts a proliferation of additional fields that could result in alterations of general relativity similar to that of the Brans-Dicke theory of the 1960s. In the presence of extra dimensions, the gravity that we feel on our four-dimensional brane of a higher dimensional world could be somewhat different from a pure four-dimensional general relativity. Some of these ideas have motivated the possibility that fundamental constants may actually be dynamical variables, and hence may vary in time or in space. However, any theoretical speculation along these lines must abide by the best current empirical bounds. Still, most of the current tests involve the weak-field, slow-motion limit of gravitational theory. Putting general relativity to the test during the 21st century is likely to involve three main themes Tests of strong-field gravity. These are tests of the nature of gravity near black holes and neutron stars, far from the weak-field regime of the solar system. Tests using gravitational waves. The detection of gravitational waves, hopefully during the next decade, will initiate a new form of astronomy but it will also provide new tests of general relativity in the highly dynamical regime. Tests of gravity at extreme scales. The detected acceleration of the universe, the observed large-scale effects of dark matter, and the possibility of extra dimensions with effects on small scales, have revealed how little precision information is known about gravity on the largest and smallest scales. In this paper we will review selected highlights of testing general relativity during the 20th century and will discuss the potential for new tests in the 21st century. We begin in

3 The Confrontation Between General Relativity and Experiment Sec. 2 with the Einstein equivalence principle, which underlies the idea that gravity and curved spacetime are synonymous, and describe its empirical support. Section 3 describes solar system tests of gravity in terms of experimental bounds on a set of parametrized post- Newtonian (PPN) parameters. In Sect. 4 we discuss tests of general relativity using binary pulsar systems. Section 5 describes tests of gravitational theory that could be carried out using future observations of gravitational radiation, and Sect. 6 describes the possibility of performing strong-field tests of general relativity. Tests of gravity at cosmological and submillimeter scales are significant topics in their own right and are beyond the scope of this paper. Concluding remarks are made in Sect. 7. For further discussion of topics in this paper, and for references to the primary literature, the reader is referred to Theory and Experiment in Gravitational Physics (Will 1993) and to the living review articles by Will (2006a), Stairs (2008), Psaltis (2008) and Mattingly (2005). 2 The Einstein Equivalence Principle and Metric Theories of Gravity The Einstein equivalence principle (EEP) is a powerful and far-reaching principle, which states that (i) test bodies fall with the same acceleration independently of their internal structure or composition (Weak Equivalence Principle, or WEP); (ii) the outcome of any local non-gravitational experiment is independent of the velocity of the freely-falling reference frame in which it is performed (Local Lorentz Invariance, or LLI); and (iii) the outcome of any local non-gravitational experiment is independent of where and when in the universe it is performed (Local Position Invariance, or LPI). The Einstein equivalence principle is central to gravitational theory, for it is possible to argue convincingly that if EEP is valid, then gravitation must be described by metric theories of gravity, which state that (i) spacetime is endowed with a symmetric metric, (ii) the trajectories of freely falling bodies are geodesics of that metric, and (iii) in local freely falling reference frames, the non-gravitational laws of physics are those written in the language of special relativity. General relativity is a metric theory of gravity, but so are many others, including the Brans-Dicke theory. To illustrate the high precisions achieved in testing EEP, we shall review tests of the weak equivalence principle, where one compares the acceleration of two laboratorysized bodies of different composition in an external gravitational field. A measurement or limit on the fractional difference in acceleration between two bodies yields a quantity η 2 a 1 a 2 / a 1 + a 2, called the Eötvös ratio, named in honor of Baron von Eötvös, the Hungarian physicist whose experiments carried out with torsion balances at the end of the 19th century were the first high-precision tests of WEP (see Fig. 1). Later classic experiments by Dicke and Braginsky in the 1960s and 1970s improved the bounds by several orders of magnitude. Additional experiments were carried out during the 1980s as part of a search for a putative fifth force, that was motivated in part by a reanalysis of Eötvös original data (the range of bounds achieved during that period is shown schematically in the region labeled fifth force in Fig. 1). The best limit on η currently comes from the Eöt Wash experiments carried out at the University of Washington, which used a sophisticated torsion balance tray to compare the accelerations of bodies of different composition toward the Earth, the Sun and the galaxy. Another strong bound comes from Lunar laser ranging (LLR), which checks the equality of free fall of the Earth and Moon toward the Sun. The results from laboratory and LLR experiments are: η Eöt Wash < , η LLR < (1)

4 C.M. Will Fig. 1 Selected tests of the Weak Equivalence Principle, showing bounds on the fractional difference in acceleration of different materials or bodies. Blue line and shading shows evolving bounds on WEP for the Earth and the Moon from Lunar laser ranging (LLR) In fact, by using laboratory materials whose composition mimics that of the Earth and Moon, the Eöt Wash experiments permit one to infer an unambiguous bound from Lunar laser ranging on the universality of acceleration of gravitational binding energy at the level of (test of the Nordtvedt effect see Sect. 3 and Table 1). The Apache Point Observatory for Lunar Laser-ranging Operation (APOLLO) project, a joint effort by researchers from the Universities of Washington, Seattle, and California, San Diego, plans to use enhanced laser and telescope technology, together with a good, highaltitude site in New Mexico, to improve the Lunar laser-ranging bound by as much as an order of magnitude. High-precision WEP experiments, can test superstring inspired models of scalar-tensor gravity, or theories with varying fundamental constants in which weak violations of WEP can occur via non-metric couplings. The project MICROSCOPE, designed to test WEP to apartin10 15 has been approved by the French space agency CNES for a 2012 launch. A proposed NASA-ESA Satellite Test of the Equivalence Principle (STEP) seeks to reach the level of η< Very stringent constraints on Local Lorentz Invariance have been placed, notably by experiments that exploited laser-cooled trapped atoms to search for variations in the relative frequencies of different types of atoms as the Earth rotates around our velocity vector relative to the mean rest frame of the universe (as determined by the cosmic background radiation). For a review, see Will (2006b). Local Position Invariance has also been tested by gravitational redshift experiments and by tests of variations with cosmic time of fundamental constants. For a review of such tests, see Uzan (2003).

5 The Confrontation Between General Relativity and Experiment Fig. 2 Measurements of the coefficient (1 + γ)/2 from observations of the deflection of light and of the Shapiro delay in propagation of radio signals near the Sun. The general relativity prediction is unity 3 Solar-System Tests of Weak-Field Gravity It was once customary to discuss experimental tests of general relativity in terms of the three classical tests, the gravitational redshift, which is really a test of the EEP, not of general relativity itself; the perihelion advance of Mercury, the first success of the theory; and the deflection of light, whose measurement in 1919 made Einstein a celebrity. However, the proliferation of additional tests as well as of well-motivated alternative metric theories of gravity, made it desirable to develop a more general theoretical framework for analyzing both experiments and theories. This parametrized post-newtonian (PPN) framework dates back to Eddington in 1922, but was fully developed by Nordtvedt and Will in the period When we confine attention to metric theories of gravity, and further focus on the slow-motion, weak-field limit appropriate to the solar system and similar systems, it turns out that, in a broad class of metric theories, only the values of a set of numerical coefficients in the expression for the spacetime metric vary from theory to theory. The framework contains ten PPN parameters: γ, related to the amount of spatial curvature generated by mass; β, related to the degree of non-linearity in the gravitational field; ξ, α 1, α 2,andα 3, which determine whether the theory violates local position invariance or local Lorentz invariance in gravitational experiments (violations of the Strong Equivalence Principle); and ζ 1, ζ 2, ζ 3 and ζ 4,which describe whether the theory has appropriate momentum conservation laws. In general relativity, γ = 1, β = 1, and the remaining parameters all vanish. For a complete exposition of the PPN framework see Will (1993). To illustrate the use of these PPN parameters in experimental tests, we cite the deflection of light by the Sun, an experiment that made Einstein an international celebrity when the sensational news of the Eddington-Crommelin eclipse measurements was relayed in

6 C.M. Will November 1919 to a war-weary world. For a light ray which passes a distance d from the Sun, the deflection is given by ( ) 1 + γ 4GM θ = 2 dc 2 ( ) ( ) 1 + γ R = arcsec, (2) 2 d where M and R are the mass and radius of the Sun and G and c are the Newtonian gravitational constant and the speed of light. The 1/2 part of the coefficient can be derived by considering the Newtonian deflection of a particle passing by the Sun, in the limit where the particle s velocity approaches c; this was first calculated independently by Henry Cavendish and Johann von Soldner around The second γ/2 part comes from the bending of straight lines near the Sun relative to lines far from the Sun, as a consequence of space curvature. A related effect, called the Shapiro time delay, an excess delay in travel time for light signals passing by the Sun, also depends on the coefficient (1 + γ)/2. To illustrate the dramatic progress of experimental gravity since the dawn of Einstein s theory, Fig. 2 shows a history of results for (1 + γ)/2. Optical denotes measurements using visible light, made mainly during solar eclipses, beginning with the 1919 measurements of Eddington and his colleagues. Arrows denote values well off the chart from one of the 1919 eclipse expeditions and from others through Radio denotes interferometric measurements of radio-wave deflection, and VLBI denotes Very Long Baseline Radio Interferometry, culminating in a global analysis of VLBI data on 541 quasars and compact radio galaxies distributed over the entire sky, which verified GR at the 0.02 percent level. Hipparcos denotes the European optical astrometry satellite. Shapiro time delay measurements began in the late 1960s, by bouncing radar signals off Venus and Mercury; the most recent test used tracking data from the Cassini spacecraft on its way to Saturn, yielding a result at the percent level. Other experimental bounds on the PPN parameters, all consistent with general relativity, came from measurements of the perihelion-shift of Mercury, bounds on the Nordtvedt effect (a possible violation of the weak equivalence principle for self-gravitating bodies) via Lunar laser ranging, and geophysical and astronomical observations. The current bounds are summarized in Table 1. The perihelion advance of Mercury, the first of Einstein s successes, is now known to agree with observation to a few parts in Although there was controversy during the 1960s about this test because of Dicke s claims of an excess solar oblateness, which would result in an unacceptably large Newtonian contribution to the perihelion advance, it is now known from helioseismology that the oblateness is of the order of a few parts in 10 7,as expected from standard solar models, and too small to affect Mercury s orbit, within the experimental error. Scalar-tensor theories of gravity are characterized by a coupling function ω(φ) whose size is inversely related to the strength of the scalar field relative to the metric. In the solar system, the parameter γ 1, for example is equal to 1/(2 + ω(φ 0 )),whereφ 0 is the value of the scalar field today outside the solar system. Solar-system experiments (primarily the Cassini results) constrain ω(φ 0 )> Proposals are being developed for advanced space missions which will have tests of PPN parameters as key components, including GAIA, a high-precision astrometric telescope (successor to Hipparcos), which could measure light-deflection and γ to the 10 6 level, the

7 The Confrontation Between General Relativity and Experiment Table 1 Current limits on the PPN parameters a Here η = 4β γ 3 10ξ/3 α 1 2α 2 /3 2ζ 1 /3 ζ 2 /3 Parameter Effect Limit Remarks γ 1 (i) time delay Cassini tracking (ii) light deflection VLBI β 1 (i) perihelion shift assumes J 2 = 10 7 from helioseismology (ii) Nordtvedt effect η = 4β γ 3 assumed ξ Earth tides 10 3 gravimeter data α 1 orbital polarization 10 4 Lunar laser ranging PSR J α 2 solar spin precession alignment of Sun and ecliptic α 3 pulsar acceleration pulsar P statistics η a Nordtvedt effect Lunar laser ranging ζ combined PPN bounds ζ 2 binary motion P p for PSR ζ 3 Newton s 3rd law 10 8 Lunar acceleration ζ 4 not independent Laser Astrometric Test of Relativity (LATOR), a mission involving laser ranging to a pair of satellites on the far side of the Sun, which could measure γ to a part in 10 8, and could possibly detect second-order effects in light propagation, and BepiColombo, a Mercury orbiter mission planned for the 2012 time frame, which could, among other measurements, determine J 2 of the Sun to 10 8, and improve bounds on a time variation of the gravitational constant. The ground-based laser ranging program APOLLO could improve the bound on the Nordtvedt parameter η to the level. The NASA mission called Gravity Probe-B completed the flight portion of its mission to measure the Lense-Thirring and geodetic precessions of gyroscopes in Earth orbit in the fall of Launched on April 20, 2004 for a 16-month mission, it consisted of four spherical fused quartz rotors coated with a thin layer of superconducting niobium, spinning at Hz, in a spacecraft containing a telescope continuously pointed toward a distant guide star (IM Pegasi). Superconducting current loops encircling each rotor measured the change in direction of the rotors by detecting the change in magnetic flux through the loop generated by the London magnetic moment of the spinning superconducting film. The spacecraft orbited the Earth in a polar orbit at 650 km altitude. The proper motion of the radio-emitting guide star relative to distant quasars was measured before, during and after the mission using VLBI. The primary science goal of GPB was a one-percent measurement of the 41 milliarcsecond per year frame dragging or Lense-Thirring effect caused by the rotation of the Earth; its secondary goal was to measure to six parts in 10 5 the larger 6.6 arcsecond per year geodetic precession caused by space curvature. Final results of the experiment were expected toward the end of A complementary test of the Lense-Thirring precession, albeit with lower accuracy than the GPB goal, involved measuring the precession of the orbital planes of two Earth-orbiting laser-ranged satellites called LAGEOS, using up-to-date models of the gravitational field of the Earth in order to subtract the dominant Newtonian precession with sufficient accuracy to yield a measurement of the relativistic effect. The resulting measurement of frame dragging is at the 10 percent level.

8 C.M. Will Table 2 Parameters of selected binary pulsars Parameter Symbol Value a in Value a in PSR J Keplerian parameters Eccentricity e (4) (2) Orbital Period P b (day) (5) (2) Post-Keplerian parameters Periastron advance ω ( o yr 1 ) (5) (2) Redshift/time dilation γ (ms) (8) 0.39(2) Orbital period derivative P b (10 12 ) (9) 1.20(8) Shapiro delay (sin i) s (4) a Numbers in parentheses denote errors in last digit 4 Binary Pulsars The binary pulsar PSR , discovered in 1974 by Joseph Taylor and Russell Hulse, provided important new tests of general relativity, specifically of gravitational radiation and of strong-field gravity. Through precise timing of the pulsar clock, the important orbital parameters of the system could be measured with exquisite precision. These include nonrelativistic Keplerian parameters, such as the eccentricity e, and the orbital period (at a chosen epoch) P b, as well as a set of relativistic post-keplerian parameters (see Table 2). The first PK parameter, ω, is the mean rate of advance of periastron, the analogue of Mercury s perihelion shift. The second, denoted γ is the effect of special relativistic time-dilation and the gravitational redshift on the observed phase or arrival time of pulses, resulting from the pulsar s orbital motion and the gravitational potential of its companion. The third, P b, is the rate of decrease of the orbital period; this is taken to be the result of gravitational radiation damping (apart from a small correction due to galactic differential rotation). Two other parameters, s and r, are related to the Shapiro time delay of the pulsar signal if the orbital inclination is such that the signal passes in the vicinity of the companion; s is a direct measure of the orbital inclination sin i. According to general relativity, the first three post-keplerian effects depend only on e and P b, which are known, and on the two stellar masses which are unknown. By combining the observations of PSR with the general relativity predictions, one obtains both a measurement of the two masses, and a test of the theory, since the system is overdetermined. The results are m 1 = ± M, m 2 = ± M, Pb GR / P b OBS = ± (3) The accuracy in measuring the relativistic damping of the orbital period is now limited by uncertainties in our knowledge of the relative acceleration between the solar system and the binary system as a result of galactic differential rotation. The results also test the strong-field aspects of metric gravitation in the following way: the neutron stars that comprise the system have very strong internal gravity, contributing as much as several tenths of the rest mass of the bodies (compared to the orbital energy, which is only 10 6 of the mass of the system). Yet in general relativity, the internal structure is effaced as a consequence of the Strong Equivalence Principle (SEP), a stronger version

9 The Confrontation Between General Relativity and Experiment of EEP that includes gravitationally bound bodies and local gravitational experiments. As a result, the orbital motion and gravitational radiation emission depend only on the masses m 1 and m 2, and not on their internal structure, apart from standard tidal and spin-coupling effects. By contrast, in alternative metric theories, SEP is not valid in general, and internalstructure effects can lead to significantly different behavior, such as the emission of dipole gravitational radiation. Unfortunately, in the case of scalar-tensor theories of gravity, because the neutron stars are so similar in PSR (and in other double-neutron star binary pulsar systems), dipole radiation is suppressed by symmetry; the best bound on the coupling parameter ω(φ 0 ) from PSR is in the hundreds. By contrast, the close agreement of the data with the predictions of general relativity constitutes a kind of null test of the effacement of strong-field effects in that theory. However, the recent discovery of the relativistic neutron star/white dwarf binary pulsar J , with a 0.19 day orbital period, may ultimately lead to a very strong bound on dipole radiation, and thence on scalar-tensor gravity. The remarkable double pulsar J is a binary system with two detected pulsars, in a 0.10 day orbit seen almost edge on, with eccentricity e = 0.09, and a periastron advance of 17 per year. A variety of novel tests of relativity, neutron star structure, and pulsar magnetospheric physics will be possible in this system. For a review of binary pulsar tests, see Stairs (2008) and Damour (2009). 5 Gravitational-Wave Tests of Gravitation Theory The detection of gravitational radiation by ground-based laser interferometers, such as LIGO in the USA, or VIRGO and GEO in Europe, by the proposed space-based laser interferometer LISA, will usher in a new era of gravitational-wave astronomy (for a review, see Hough and Rowan 2000). Furthermore, it will yield new and interesting tests of general relativity in its radiative regime. One important test is of the speed of gravitational waves. According to general relativity, in the limit in which the wavelength of gravitational waves is small compared to the radius of curvature of the background spacetime, the waves propagate along null geodesics of the background spacetime, i.e. they have the same speed, c, as light. In other theories, the speed could differ from c because of coupling of gravitation to background gravitational fields. For example, in some theories with a flat background metric η, gravitational waves follow null geodesics of η, while light follows null geodesics of g. In brane-world scenarios, the apparent speed of gravitational waves could differ from that of light if the former can propagate off the brane into the higher dimensional bulk. Another way in which the speed of gravitational waves could differ from c is if gravitation were propagated by a massive field (a massive graviton), in which case v g would depend on the wavelength λ of the gravitational waves according to v g /c 1 λ 2 /2λ 2 g,whereλ g = h/m g c is the graviton Compton wavelength (λ g λ is assumed). The most obvious way to test for a massive graviton is to compare the arrival times of a gravitational wave and an electromagnetic wave from the same event, e.g. a supernova. For a source at a distance of hundreds of megaparsecs, and for a relative arrival time between the two signals of order seconds, the resulting bound would be of order 1 v g /c < A bound such as this cannot be obtained from solar system tests at current levels of precision. However, there is a situation in which a bound on the graviton mass can be set using gravitational radiation alone. That is the case of the inspiralling compact binary, the final stage of evolution of systems like the binary pulsar, in which the loss of energy to gravitational waves has brought the binary to an inexorable spiral toward a final merger. Because

10 C.M. Will the frequency of the gravitational radiation sweeps from low frequency at the initial moment of observation to higher frequency at the final moment, the speed of the gravitational waves emitted will vary, from lower speeds initially to higher speeds (closer to c) at the end. This will cause a distortion of the observed phasing of the waves as a function of wavelength. Furthermore, through the technique of matched filtering, whereby a theoretical model of the wave and its phase evolution is cross-correlated against the detected signal, the parameters of the compact binary can be measured accurately, along with the parameter, the graviton Compton wavelength, that governs the distortion. Advanced ground-based detectors of the LIGO-VIRGO type could place a bound λ g on the order of several times km, and the proposed space-based LISA antenna could place a bound on the order of km. These potential bounds can be compared with the solid bound λ g > km, derived from solar system dynamics, which limit the presence of a Yukawa modification of Newtonian gravity of the form V(r)= (GM/r) exp( r/λ g ), and with the model-dependent bound λ g > km from consideration of galactic and cluster dynamics. 6 Tests of Gravity in the Strong-Field Regime One of the main difficulties of testing GR in the strong-field regime is the possibility of contamination by uncertain or complex physics. In the solar system, weak-field gravitational effects could in most cases be measured cleanly and separately from non-gravitational effects. The remarkable cleanliness of the binary pulsar permitted precise measurements of gravitational phenomena in a strong-field context. Unfortunately, nature is rarely so kind. Still, under suitable conditions, qualitative and even quantitative strong-field tests of GR could be carried out. One example is the exploration of the spacetime near black holes and neutron stars via accreting matter. Studies of certain kinds of accretion known as advection-dominated accretion flow (ADAF) in low-luminosity binary X-ray sources may yield the signature of the black hole event horizon. The spectrum of frequencies of quasi-periodic oscillations (QPO) from galactic black hole binaries may permit measurement of the spins of the black holes. Aspects of strong-field gravity and frame-dragging may be revealed in spectral shapes of iron fluorescence lines from the inner regions of accretion disks around black holes and neutron stars. Measurements of the detailed shape of the infrared image of the accretion flow around the massive black hole in the center of our galaxy could also provide tests of the spacetime black hole metric. Because of uncertainties in the detailed models, the results to date of studies like these are suggestive at best, but the combination of higher-resolution observations and better modelling could lead to striking tests of strong-field predictions of GR. For a review of such tests see Psaltis (2008). The best tests of GR in the strong field limit may come from gravitational-wave observations. The ground-based interferometers may detect the gravitational waves from the final inspiral and merger of a pair of stellar-mass black holes. Comparison of the observed waveform with the predictions of GR from a combination of analytic and numerical techniques may provide a test of the theory in the most dynamical, strong-field limit. The proposed space antenna LISA may observe as many as 100 mergers of massive black holes per year, with large signal-to-noise ratio. Such observations could provide precise measurements of black hole masses and spins, and could test the no hair theorems of black holes by detecting the spectrum of quasi-normal ringdown modes emitted by the final black hole. Observations by LISA of the hundreds of thousands of gravitational-wave cycles emitted

11 The Confrontation Between General Relativity and Experiment when a small black hole inspirals onto a massive black hole could test whether the geometry of a black hole actually corresponds to the hair-free Kerr metric. 7 Conclusions Einstein s general theory of relativity altered the course of science. It was a triumph of the imagination and of theory, but in the early years following its formulation, experiment played a secondary role. In the final four decades of the 20th century, we witnessed a second triumph for Einstein, in the systematic, high-precision experimental verification of general relativity. It has passed every test with flying colors. But the work is not done. During the 21st century, we may look forward to the possibility of tests of strong-field gravity in the vicinity of black holes and neutron stars. Gammaray, X-ray and gravitational-wave astronomy will play a critical role in probing this largely unexplored aspect of general relativity. General relativity is now the standard model of gravity. But as in particle physics, there may be a world beyond the standard model, beyond Einstein. Quantum gravity, strings and branes may lead to testable effects beyond standard general relativity. Experimentalists and observers can be counted on to continue a vigorous search for such effects using laboratory experiments, particle accelerators, gravitational-wave detectors, space telescopes and cosmological observations, well into the 21st century. Acknowledgements This work was supported in part by the US National Science Foundation, Grant No. PHY and by the National Aeronautics and Space Administration, Grant No. NNG-06GI60G. We are grateful for the hospitality of the Institut d Astrophysique de Paris, where this paper was prepared. This review is based in large measure on a paper prepared for the proceedings of the conference Beyond Einstein: Perspectives on Geometry, Gravitation and Cosmology in the Twentieth Century, held in Mainz, Germany, September 22-26, References T. Damour, in Physics of Relativistic Objects in Compact Binaries: from Birth to Coalescence: Astrophysics and Space Science Library, vol. 359, ed. by M. Colpi, P. Casella, V. Gorini, U. Moschella, A. Possenti, (Springer, New York, 2009, in press) J. Hough, S. Rowan, Living Rev. Relativ. 3, 3 (2000) [On-line article] Cited on 1 November 2008, D. Mattingly, Living Rev. Relativ. 8, 5 (2005) [On-line article] Cited on 1 November 2008, D. Psaltis, Living Rev. Relativ. 11, 9 (2008) [On-line article] Cited on 1 November 2008, org/lrr I.H. Stairs, Living Rev. Relativ. 6, 5 (2008) [On-line article] Cited on 1 November 2008, org/lrr J.-P. Uzan, Rev. Mod. Phys. 75, 403 (2003) C.M.Will,Theory and Experiment in Gravitational Physics (Cambridge University Press, Cambridge, 1993) C.M. Will, Living Rev. Relativ. 9, 3 (2006a) [Online article]: Cited on 1 November 2008, org/lrr C.M. Will, in Einstein : Poincaré Seminar 2005, ed. by T. Damour, O. Darrigol, B. Duplantier, V. Rivasseau (Birkhäuser, Switzerland, 2006b), p. 33